Contest Win Probabilities and Ability Calibration

Solves the horse race problem in both directions. Infers relative ability from win probabilities (or betting dividends) for contests whose entrants share a common performance distribution, with dead heats handled exactly, by the lattice fixed-point algorithm of Cotton (2021) . Also computes all N win probabilities of a factor-structured Gaussian race (multinomial probit with low-rank-plus-diagonal covariance) in one shared-lattice pass of O(Q*N*L) operations, and inverts observed shares to abilities by a damped Newton method with analytic slopes. A dependency-free base-R port of the reference python package 'winning'. Performances are times: lowest wins.

winning (R package)

All N win probabilities of a factor-structured Gaussian race (multinomial probit with covariance VV' + diag(D)) in one shared-lattice pass, and the inverse: calibrating abilities from observed shares.

nodes <- hermite_nodes(2)
p <- win_probabilities_factor(mu, V, D, nodes)      # min wins; negate mu for argmax
a <- abilities_from_probabilities_factor(p, V, D, nodes)

Why not N calls to mvtnorm::pmvnorm? That computes the same numbers (agreement to ~1e-6 at N = 5, verified in the test suite) but pays for N separate (N-1)-dimensional integrals; the shared survival field prices every alternative from one O(Q N L) pass. At N = 200 the difference is seconds versus minutes; at N = 1000, seconds versus hours.

Pure base R, no dependencies (mvtnorm suggested for the cross-check tests only). The Python/Rust implementations, benchmarks, and the paper live in the parent repository.

CRAN preparation checklist: roxygenize man pages, add vignette, R CMD check --as-cran, submit.